Transmission of data (input data) through a channel typically involves coding and modulation. Coding generally changes the representation of the input data to a format whose characteristics are better suited to withstand the noise characteristics of the channel. Modulation takes the coded digital data and converts it to an analog radio wave.
Multiple carrier modulation techniques, e.g., orthogonal frequency division multiplexing (OFDM), are generally known. An example of a modulation technique generally known per se, and generally known-to-be used-with OFDM, is quadrature amplitude modulation (QAM).
For example, 16 QAM can transfer up to 16 (=24) different types of symbols on a given sub-channel of, e.g., an OFDM-coded signal. FIG. 1 depicts a constellation 100 of symbols 102 corresponding to 16QAM, according to the Background Art. Each symbol 102 is centered in a cell 110. Symbols are identified by Cartesian coordinates that assume a unit value of R (to be discussed further below). A received signal vector is represented by a vector in polar notation (amplitude, phase). Assuming an ideal and noiseless channel, two example received signal vectors 106 and 108 having coordinates (√{square root over (2)}R, θ1) and (3√{square root over (2)}R, θ2), respectively, are depicted. Because an ideal, noiseless channel is assumed, received signal vectors 106 and 108 are mapped exactly to symbols (R,R) and (−3R,3R), respectively.
A real channel is not ideal. So before sending input data through a real channel, a training or initializing process is performed on the channel to determine an amount that the channel should be expected to change the amplitude
  (      Δ    ⁢                  ⁢          A      CH      expected        )and phase
  (      Δ    ⁢                  ⁢          Θ      CH      expected        )of a transmitted signal vector (TV), i.e., to determine the transfer function
  (      H    CH    noiseless    )of the real but (assumed) noiseless channel.
                              H          CH          noiseless                =                  f          ⁡                      (                                          Δ                ⁢                                                                  ⁢                                  A                  CH                  expected                                            ,                              Δ                ⁢                                                                  ⁢                                  Θ                  CH                  expected                                                      )                                              (        1        )            A Background Art receiver then compensates the received vector (RV) by the expected amounts of change to produce a corresponding expected (compensated) vector (EV), i.e., to decode RV. Assuming a noiseless channel, FIG. 2 depicts such a non-ideal channel compensation scheme according to the Background Art. In FIG. 2, received vector RV would have been mapped into cell 110A, but compensated vector EV is mapped to polar coordinates (√{square root over (2)}R, θ1) in cell 110B, which identifies symbol (R,R) as corresponding to RV.
A real channel also is not noiseless. Hence, received vector is more accurately described as follows.
                    RV        =                                            H              CH              noiseless                        ·            TV                    +          NV                                    (        2        )            What otherwise would have been a compensated vector EV for a noiseless channel is now described as an equivalent vector (EQV), as follows.EQV=EVnoiseless+NV  (3)Equivalent vector EQV will typically not map directly to a symbol because of noise in the channel. According to the Background Art, the cell into which compensated vector EQV maps is considered to determine the symbol which compensated vector EQV represents. In other words, received vector RV is decoded by assuming that equivalent vector EQV represents the symbol of the cell in which EQV is mapped. Up to an amplitude R of noise can be decoded with high confidence. Such a decoding scheme is depicted in Background Art FIG. 3 for cell 110i. 